Showing papers in "Journal of Thermal Stresses in 1996"
TL;DR: In this article, an unconstrained elastic layer under statically self-equilibrating thermal or residual stresses is considered, where the layer is assumed to be a functionally graded material (FGM), meaning that its thermo-mechanical properties are continuous functions of the thickness coordinate.
Abstract: In this study an unconstrained elastic layer under statically self-equilibrating thermal or residual stresses is considered. The layer is assumed to be a functionally graded material (FGM), meaning that its thermo-mechanical properties are assumed to be continuous functions of the thickness coordinate. The layer contains an embedded or a surface crack perpendicular to its boundaries. Using superposition the problem is reduced to a perturbation problem in which the crack surface tractions are the only external forces. The dimensions, geometry, and loading conditions of the original problem are such that the perturbation problem may be approximated by a plane strain mode I crack problem for an infinite layer. After a general discussion of the thermal stress problem, the crack problem in the nonhomogeneous medium is formulated. With the application to graded coatings and interfacial zones in mind, the thickness variation of the thermo-mechanical properties is assumed to be monotonous. Thus, the functions suc...
331 citations
TL;DR: In this article, the authors analyzed thermal stresses and the stress intensity factor in an edge-cracked strip of a functionally graded material (FGM) subjected to sudden cooling at the cracked surface.
Abstract: We analyze thermal stresses and the stress intensity factor in an edge-cracked strip of a functionally graded material (FGM) subjected to sudden cooling at the cracked surface. It is assumed that the shear modulus of the material decreases hyperbolically with the higher value at the surface exposed to the thermal shock and that the thermal conductivity varies exponentially. Volume fractions of the constituents in a ceramic-metal FGM are then determined with the assumed shear modulus gradient using a three-phase model of conventional composites. The differences between the other assumed material properties and those predicted by the three-phase model are delineated and the applicability of the assumed FGM is discussed. It is shown that the maximum tensile thermal stress in the strip without cracks is substantially reduced by the assumed thermal conductivity gradient and that the magnitude of the compressive stress is increased. A strong compressive zone just away from the thermally shocked surface is devel...
176 citations
TL;DR: In this article, a nonhomogeneous plate made of Zirconium Oxide and Titanium alloy is analyzed theoretically, and the thermal stress distribution is formulated under the mechanical of traction-free condition.
Abstract: Nonhomogeneous materials, such as functionally gradient materials (FGM), have special characteristics due to arbitrarily distributed and continuously varied material properties. For such nonhomogeneous materials, the heat conduction equation is presented in a nonlinear form. In this paper, the temperature solution for such a nonlinear system is formulated approximately, and the solution of the integral form of nonuniform thermal material constants is given. Taking into account the effect of temperature dependency of material properties, the one-dimensional transient heat conduction problem of such a nonhomogeneous plate is analyzed theoretically, and the associated thermal stress distribution is formulated under the mechanical of traction-free condition. Numerical calculations are carried out for a nonhomogeneous plate made of Zirconium Oxide and Titanium alloy. The influence of a temperature dependency in material properties and of a change of nonhomogeneity affected by the temperature and the thermal st...
154 citations
TL;DR: In this article, the exact solution to the problem of uniform heating of a spherical body whose elastic moduli and thermal expansion coefficient vary linearly with the radius was presented, where the Frobenius series method was used to find exact expressions for the displacements and stresses.
Abstract: We present the exact solution to the problem of uniform heating of a spherical body whose elastic moduli and thermal expansion coefficient vary linearly with the radius. The Frobenius series method is used to find exact expressions for the displacements and stresses. Both the radial and hoop stresses are largest in magnitude at the center of the sphere. The radial stress decays to zero at the outer edge, whereas the hoop stresses always change sign at some intermediate value of the radius. We also find an exact expression for the effective thermal expansion coefficient. For the special case where the thermal expansion coefficient varies with the radius but the elastic moduli are uniform, the effective thermal expansion coefficient of the sphere is equal to the volumetric average of the local thermal expansion coefficient. In the more general case, where the moduli also vary, the moduli variations have very little influence on the effective thermal expansion coefficient.
119 citations
TL;DR: In this article, the effect of two relaxation times, following Green and Lindsay's theory, on the reflection of thermoelastic waves at a homogeneous, isotropic, and thermally conducting elastic solid half-space is studied.
Abstract: The effect of two relaxation times, following Green and Lindsay's theory, on the reflection of thermoelastic waves at a homogeneous, isotropic, and thermally conducting elastic solid half-space is studied. The results for the partition of the energy for various values of the angle of incidence are presented and compared with that of Lord and Shulman's theory to show the importance of the second relaxation time.
109 citations
TL;DR: In this paper, the linear theory of thermoelasticity without energy dissipation for homogeneous and isotropic materials is employed to study one-dimensional waves in a half-space.
Abstract: The linear theory of thermoelasticity without energy dissipation for homogeneous and isotropic materials is employed to study one-dimensional waves in a half-space The waves are supposed to be due to sudden inputs of temperature and stress/strain on the boundary The Laplace transform method is employed to solve the problem Exact solutions, in closed form, for the displacement, temperature, strain, and stress fields are obtained The characteristic features of the underlying theory are analyzed in light of these solutions and their counterparts in earlier works
104 citations
TL;DR: In this paper, an initial boundary value problem in terms of stress and entropy-flux is formulated and the uniqueness of its solution established in the context of the linear theory of thermoelasticity without energy dissipation.
Abstract: In the context of the linear theory of thermoelasticity without energy dissipation for homogeneous and isotropic materials, an initial boundary value problem in terms of stress and entropy-flux is formulated and the uniqueness of its solution established.
98 citations
TL;DR: In this article, the Euler equations are applied to the functional of energy, and the general thermoelastic equations of nonlinear shell theory are obtained and compared with the Donnel equations.
Abstract: The nonlinear strain-displacement relations in general cylindrical coordinates are simplified by Sander's assumptions for the cylindrical shells and substituted into the total potential energy function for thermoelastic loading. The Euler equations are then applied to the functional of energy, and the general thermoelastic equations of nonlinear shell theory are obtained and compared with the Donnel equations. An improvement is observed in the resulting equations as no length limitations are imposed on a thin cylindrical shell. The stability equations are then derived through the second variation of potential energy, and the same improvements are extended to the resulting thermoelastic stability equations. Based on the improved equilibrium and stability equations, the magnitude of thennoelastic buckling of thin cylindrical shells under different thermal loadings is obtained. The results are extended to short and long thin cylindrical shells.
56 citations
TL;DR: In this article, the Laplace transform is used to solve two problems of a solid sphere and of an infinite space with a spherical cavity, where the surface in each case is taken to be tractionfree and subjected to a given axisymmetric temperature distribution.
Abstract: Two-dimensional thermoelastic problems under axisymmetric temperature distributions are considered within the context of the theory of generalized thermoelasticity with one relaxation time. The general solution is obtained in the Laplace transform domain by using a direct approach without the customary use of potential functions. The resulting formulation is used to solve two problems of a solid sphere and of an infinite space with a spherical cavity. The surface in each case is taken to be tractionfree and subjected to a given axisymmetric temperature distribution. The inversion of the Laplace transforms are carried out using the inversion formula of the transform together with Fourier expansion techniques. Numerical methods are used to accelerate the convergence of the resulting series to obtain the temperature, displacement, and stress distributions in the physical domain. Numerical results are represented graphically and discussed. A comparison is made with the solution of the corresponding coupled pr...
50 citations
TL;DR: By means of elementary functions, the fundamental solution of equations of the thermoelasticity of the steady oscillations for a mixture of two elastic solids is constructed, and basic properties are established as discussed by the authors.
Abstract: By means of elementary functions, the fundamental solution of equations of the thermoelasticity of the steady oscillations for a mixture of two elastic solids is constructed, and basic properties are established.
49 citations
TL;DR: In this paper, the problem of thermal stresses for isotropic microstretch elastic cylinders subjected to a temperature distribution that is linear in the axial coordinate was addressed and a direct method was used to reduce the problem to solving plane strain problems.
Abstract: This article addresses the problem of thermal stresses for isotropic microstretch elastic cylinders subjected to a temperature distribution that is linear in the axial coordinate. A direct method is used to reduce the problem to solving plane strain problems. The results are used to study the deformation of circular cylinders.
TL;DR: In this paper, the thermal postbuckling of a beam made of physically nonlinear thermoelastic material is studied and the range of a safe buckling temperature is determined.
Abstract: The thermal postbuckling of a beam made of physically nonlinear thermoelastic material is studied. The range of a safe buckling temperature is determined, and some comparisons between the nonlinear and linear postbuckling behaviors of the beam are discussed. In particular, it is shown that in a postbuckling state the beam can take many different configurations.
TL;DR: In this article, a higher-order theory for the thermoelastic response of composite materials with microstructures characterized by arbitrarily nonuniform reinforcement spacing in two directions (i.e., bidirectionalfy functionally graded materials) is further extended to accommodate the effect of inelastic responses of the constituent phases.
Abstract: A recently developed higher order theory for the thermoelastic response of composite materials with microstructures characterized by arbitrarily nonuniform reinforcement spacing in two directions (i.e., bidirectionalfy functionally graded materials) is further extended to accommodate the effect of an inelastic response of the constituent phases. This theory circumvents the problematic use of the standard micromechanical approach, based on the concept of a representative volume element, commonly employed in the analysis of functionally graded composites by explicitly coupling the local (microstructural) and global (macrostructural) responses. The theoretical framework is based on volumetric averaging of the various field quantities together with the imposition of boundary and interfacial conditions in an average sense between the subvolumes used to characterize the composite's functionally graded microstructure. Examples are presented that illustrate how the presence of plasticity and microstructure affect...
TL;DR: In this article, the authors considered the crack problem in semi-infinite functionally graded materials (FGMs) under thermal load and the main objective was to reduce the thermal stress by assigning an appropriate value of the coefficient of thermal expansion.
Abstract: The crack problem in semi-infinite functionally graded materials (FGMs) under thermal load is considered The main objective of this work is to reduce the thermal stress by assigning an appropriate value of the coefficient of thermal expansion, which changes in two directions. It is assumed that the coefficient of thermal expansion is exponentially dependent on x- and y-directions as $. From the formulation of the problem it reduces to a singular integral equation with a simple Cauchy type kernel. This singular integral equation has the derivative of the crack surface displacement as the density function. The thermal stress intensity factor can be calculated versus the mechanical nonhomogeneous parameters of the assumed FGMfrom the solution of the singular integral equation. Then from the calculated values of the thermal stress intensity factor the appropriate values of the nonhomogeneous parameters of the coefficient of thermal expansion and the mechanical nonhomogeneous parameters of the material can be ...
TL;DR: In this paper, the similarity that exists between the thermoelastic and piezoelastic formulations is exploited in establishing solutions for cylindrical bending of piezother-melastic laminates exposed to combined thermo-electro-mechanical loads.
Abstract: Exact analytical solutions are given for stationary two-dimensional temperature, stress, and displacement distributions in hybrid laminates containing isotropic and/or orthotropic layers. The similarity that exists between the thermoelastic and piezoelastic formulations is exploited in establishing solutions for cylindrical bending of piezother-moelastic laminates exposed to combined thermo-electro-mechanical loads. Results are compared with those based upon classical and high-order bending theories.
TL;DR: In this article, a finite element formulation of the perturbation method is presented, in which the linearity of the governing equations is exploited to obtain separated-variable solutions for perturbations with exponential variation in time.
Abstract: The steady-state conduction of heat across an interface between two contacting bodies can become unstable as a result of the interaction between thermoelastic distortion and a pressure-dependent thermal contact resistance. Analytical solutions for the stability boundary have been obtained for simple systems using perturbation methods but become prohibitively complex for finite geometries. This paper presents a finite element formulation of the perturbation method in which the linearity of the governing equations is exploited to obtain separated-variable solutions for the perturbation with exponential variation in time. The problem is thus reduced to a linear eigenvalue problem with the exponential growth rate appearing as the eigenvalue. Stability of the system requires that all eigenvalues have negative real part. The method is tested against an analytical solution of the two-dimensional problem of a strip in contact with a rigid wall. Excellent results are obtained for the stability boundary even with a...
TL;DR: In this article, an inverse thermoelastic problem in an isotropic structural plate onto which a piezoelectric ceramic plate is perfectly bonded is discussed, and the unknown heating temperature is inferred from the prescribed electric potential, and then response quantities in the thermal, elastic and electric fields are derived too.
Abstract: This article discusses an inverse thermoelastic problem in an isotropic structural plate onto which a piezoelectric ceramic plate is perfectly bonded. When unknown heating temperature acts on the free surface of the isotropic structural plate, an electric potential is induced in the piezoelectric ceramic plate. Therefore, the unknown heating temperature is inferred from the prescribed electric potential, and then response quantities in the thermal, elastic, and electric fields are derived too. Finally numerical results are illustrated graphically.
TL;DR: In this article, the effect of heat transfer by fluid flow through pores on the temperature and thermal stress distributions was investigated in a fluid-saturated porous hollow sphere subjected to a sudden rise in temperature and pressure on its inner wall.
Abstract: By using the thermoporoelastic theory proposed previously, thermal stresses are analyzed that are induced in a fluid-saturated porous hollow sphere subjected to a sudden rise in temperature and pressure on its inner wall. Since the problem formulated is spherically symmetric, the displacement field is decoupled from the temperature and pore fluid pressure fields, which are still coupled with each other. Coupled diffusion equations for heat and fluid flows are solved by the Crank-Nicolson implicit method because they involve nonlinear and integral terms. The attention is focused on the effect of heat transfer by fluid flow through pores on the temperature and thermal stress distributions. This effect is very marked for the case where the fluid diffusivity is much larger than the thermal one. This suggests a possible control of thermal stresses by active fluid injection.
TL;DR: In this article, a theory of thermoelasticity for nonsimple materials is derived within the framework of extended thermodynamics, and the theory is linearized, and a uniqueness result is presented.
Abstract: A theory of thermoelasticity for nonsimple materials is derived within the framework of extended thermodynamics. The theory is linearized, and a uniqueness result is presented. A Galerkin type solution of the field equations and fundamental solutions for steady vibrations are also studied.
TL;DR: In this article, a homogeneous and isotropic infinite body with a spherical cavity is considered for the two different theories of generalized thermoelasticity, that is, Lord and Shulman's theory and Green and Lindsay's theory.
Abstract: Thermoelastic interactions caused in a homogeneous and isotropic infinite body with a spherical cavity are considered for the two different theories of generalized thermoelasticity, that is, Lord, and Shulman's theory and Green and Lindsay's theory. Analytical expressions for the temperature, displacement, and thermal stress fields are obtained; and the results are compared with the classical dynamical coupled theory.
TL;DR: In this paper, a modal expansion technique is proposed to calculate the forced vibrations in the time domain, and the computation of the eigenvalues and eigenfunctions of the corresponding eigenvalue problem is the essential problem to be solved initially.
Abstract: The dynamic interaction of magneto-thermo-elastic waves in structural members of finite size is studied. Of special interest are the thermally induced small thickness vibrations in a planar conducting plate layer. To calculate the forced vibrations in the time domain, a modal expansion technique is proposed Therefore, the computation of the eigenvalues and eigenfunctions of the corresponding eigenvalue problem is the essential problem to be solved initially. In addition to a numerical evaluation of the algebraic eigenvalue equations, a perturbation analysis is presented to find the complex-valued eigensolutions of the problem for a weak coupling. In every case, the calculation of the forced vibrations is reduced to solving uncoupled ordinary differential equations. Finally, the complete thermally induced vibrations are represented by infinite series to be evaluated straightforwardly in a computer-aided form.
TL;DR: In this paper, finite deformations of heat conducting viscous dielectric solids are studied and linear constitutive relations valid for infinitesimal deformations are derived for each class of materials.
Abstract: We study finite deformations of heat conducting viscous dielectric solids and derive constitutive relations that satisfy an entropy inequality. These are simplified for orthotopic, transversely isotropic, and isotropic materials. For each class of materials, linear constitutive relations valid for infinitesimal deformations are derived.
TL;DR: In this paper, a mathematical model that incorporates volume relaxation is applied to predict the development of the thermal residual stresses, for a generic polycarbonate, in a thin injection-molded strip cavity.
Abstract: A mathematical model that incorporates volume relaxation is applied to predict the development of the thermal residual stresses, for a generic polycarbonate, in a thin injection-molded strip cavity. The model assumes thermo-rheological/piezo-rheological simple viscoelastic material behavior in both the deviatoric and dilatational domains, Prony-series for both the shear-relaxation and dilatational-retardation functions, a modified Gibb's function for the shift factor of both the shear-relaxation and dilatational-retardation spectra. The purpose of this study is to examine the effects of volume relaxation, imposed lateral boundary conditions, and the average shear-relaxation and dilatational-retardation times on the developed residual stresses.
TL;DR: In this paper, it was shown that the problem of unsteady thermal stress under non-uniform heat generation or with nonuniform initial temperature distribution over the region can be solved approximately without the domain integral by means of the boundary element method.
Abstract: If the initial temperature is assumed to be constant, the boundary element method (BEM) does not need the domain integral in the analyses of unsteady thermoelastic problems under no heat generation within the domain. However, under the heat generation or nonuniform initial temperature distribution, the domain integral becomes necessary. This paper shows that the problem of unsteady thermoelasticity under nonuniform heat generation or with nonuniform initial temperature distribution over the region can be solved approximately without the domain integral by means of the boundary element method. This method can also be applied to unsteady thermal stress problems under general heat generation, though for the general heat generation the domain must be divided into small domains, where distributions of heat generation satisfy the Laplace equation.
TL;DR: In this article, the free vibrations of a truncated conical thin shell subjected to thermal gradients were analyzed and the governing equations of the shell were based on the Donnell-Mushtari theory of thin shells.
Abstract: This article presents an analysis of the free vibrations of a truncated conical thin shell subjected to thermal gradients. The governing equations of the shell are based on the Donnell-Mushtari theory of thin shells. Simply supported and clamped boundary conditions are considered at both ends of truncated conical shell. Temperature loading due to supersonic flow is assumed to vary along the meridian and across the thickness of the shell Hamilton's principle is used to derive the appropriate governing equations of a conical shell with temperature-dependent material properties. The shell material has a kind of inhomogeneity due to the varying temperature load and temperature dependency of material properties. The resulting differential equations are solved numerically using the collocation method. The results are compared with certain earlier results. The influence of temperature load on the vibration characteristics is examined for the conical shells with various geometrical properties.
TL;DR: In this paper, a two-dimensional axisymmetric problem in a homogeneous transversely isotropic medium has been studied by employing the eigenvalue approach after applying the technique of Laplace and Hankel transforms.
Abstract: In this article a two-dimensional axisymmetric problem in a homogeneous transversely isotropic medium has been studied by employing the eigenvalue approach after applying the technique of Laplace and Hankel transforms. An example of infinite space with concentrated force at the origin has been presented to illustrate the application of the approach. The results for coupled thermoelasticity and in the case of a homogeneous isotropic medium have also been deduced. The results obtained can be used for a broad class of problems in generalized thermoelasticity. The integral transforms have been inverted by using a, numerical technique to obtain the displacements, temperature, and stresses in the physical domain. The results for these quantities are given and illustrated graphically.
TL;DR: In this paper, the authors investigated the three-dimensional thermal stresses induced by grinding represented by a moving triangular heat source and derived the solutions of transient thermal stresses by the Goodier's thermoelastic potential and Galerkin functions.
Abstract: Thermal stresses on a ground surface are one of the main concerns during surface grinding. The purpose of this article is to investigate the three-dimensional thermal stresses induced by grinding represented by a moving triangular heat source. The solutions of transient thermal stresses are derived by the Goodier's thermoelastic potential and Galerkin functions. The stresses are calculated numerically by the inverse Fourier transformation and integration of Simpson's 3/8 rule. Results show that the stress in the direction of the grinding depth is compressive and larger than the tensile stress along the feed direction. The stresses near the grinding zone change drastically. The workpiece feedrate is the main factor affecting the normal stresses. Cooling is essential in surface grinding, which can effectively reduce the normal stresses to zero or perhaps to negative value.
TL;DR: In this article, the problem of steady-state thermal stress in a long cylinder with N equally spaced longitudinal circular cylindrical cavities is solved using a special class of basis functions of Laplace and biharmonic equations.
Abstract: Using a special class of basis functions of Laplace and biharmonic equations, the problems of steady-state thermal stress in a long cylinder with N equally spaced longitudinal circular cylindrical cavities are solved. It is assumed that the inner and outer surfaces of the cylinder are free from external tractions. It is also assumed that the properties of the material of the cylinder are independent of temperature and that the material is linearly elastic and isotropic. The two cases when (1) the temperatures of the inner surfaces are all the same but different from that of the outer surface and (2) the temperatures of the inner surfaces are the same and the outer surface is subject to convection are investigated. The basis functions for Airy stress function φ are derived in closed form for both cases (1) and (2). The basis functions for the temperature T¯; are also obtained in closed form except when the Biot number BI is a noninteger in case (2). For these cases of noninteger BI, the functions of T¯ are...
TL;DR: In this article, the effects of thermal expansion and drying contraction on the clay cracking are discussed in detail, and it is shown that the effect of thermal contraction on cracking is much smaller than that of drying expansion, even at high temperatures.
Abstract: Hydrothermal stresses in a clay put in a high-speed drying furnace are discussed. This practical clay is treated as a hygrothermal elastic material that has a simple shape of an infinite body with a bored cylindrical hole. Thus, a theory of hygrothermoelasticity with uneven distributions of temperature and moisture concentration is used to find a closed-form hygrothermal hoop stress in such a body and to illustrate the solution graphically. For a clay put into a high-speed drying furnace, the effects of thermal expansion and drying contraction on the clay cracking are discussed in detail. In particular, it is shown that the effect of thermal expansion on cracking is much smaller (only a few percent) than that of drying contraction, even at high temperatures. As a result, the clay cracking under practical drying conditions would be caused by a drying stress concentration.
TL;DR: In this paper, the residual stress distribution in a long aluminum solid cylinder subjected to rapid cooling was evaluated using a numerical method. But, the authors did not consider the post-yielding problem.
Abstract: A numerical method is presented for evaluating the residual stress distribution in a long aluminum solid cylinder subjected to rapid cooling. An analytical model is developed for the temperature distribution. For the boundary conditions, experimental data for the outer surface of the cylinder are used and a reasonable agreement between the predicted temperature distribution at the center of the cylinder and the experimental data is observed. For the numerical analysis, a quasi-static, uncoupled thermoelastoplastic analysis, based on a hyperbolic sine law, is presented. The numerical results are presented for the temperature distribution as well as the thermoelastoplastic stress distribution in a solid cylinder with temperature-dependent properties. The residual stress distribution is compared with the results of other investigators who used the Finite Element Method, and a reasonable agreement between our results and previous results is observed. The conclusion is reached that the temperature dependency of the yield stresses and the problem of post-yielding are two important factors to be considered when developing a model for predicting the residual stresses in quenched bodies.